Question

6.9.4 quiz: more than one vertical asymptote
question 10 of 10
to make a sketch of any rational function whose numerator is a number and whose denominator is a factored polynomial, use the following rule of thumb:
the function has a vertical asymptote at every x - value where its numerator is zero, and you can make a table for each vertical asymptote to find out what happens to the function there.
a. true
b. false

Explanation:

Step1: Recall the rule for vertical asymptotes

A rational function \(y = \frac{f(x)}{g(x)}\) has a vertical asymptote at \(x = a\) when \(g(a)=0\) and \(f(a)
eq0\). The statement in the question says "The function has a vertical asymptote at every \(x\) - value where its numerator is zero", which is incorrect. The vertical asymptote occurs at the \(x\) - values where the denominator is zero (and the numerator is non - zero at those \(x\) - values).

Answer:

B. False